A few recommendations to make completing these missions a bit easier:
1. Take over the districts in the areas that the missions take place. Much easier to have your buddies shooting gangsters/cops than to have enemy gangsters shooting you.
2. Bring along as many gang members as you can. You may quickly run out of ammo if you don't. All you have to do is shoot the target vehicle once, and your buddies will unload on the car and its occupants.
3. If nearby, use the Forgive and Forget and Rim Jobs locations, especially on the higher levels.
4. Grab a police car or other fast car to use when chasing down the target vehicle. The cars they give you (e.g., the Zimos) are comparatively slow and unwieldy.